library(dplyr)
# For Model fitting
library(lme4)
library(purrr)
# For diagnostics
library(performance)
# For adding new columns
library(tibble)
library(caret)# Load data
sys.source("./scripts/code_join_data_full_dataset.R", envir = knitr::knit_global())# Load functions
## Models
sys.source("./R/functions_models.R", envir = knitr::knit_global())Select performance and traits variables
Transform variables
Back transformation
Even though you’ve done a statistical test on a transformed variable, such as the log of fish abundance, it is not a good idea to report your means, standard errors, etc. in transformed units. A graph that showed that the mean of the log of fish per 75 meters of stream was 1.044 would not be very informative for someone who can’t do fractional exponents in their head. Instead, you should back-transform your results. This involves doing the opposite of the mathematical function you used in the data transformation. For the log transformation, you would back-transform by raising 10 to the power of your number. For example, the log transformed data above has a mean of 1.044 and a 95% confidence interval of ±0.344 log-transformed fish. The back-transformed mean would be 101.044=11.1 fish. The upper confidence limit would be 10(1.044+0.344)=24.4 fish, and the lower confidence limit would be 10(1.044-0.344)=5.0 fish. Note that the confidence interval is not symmetrical; the upper limit is 13.3 fish above the mean, while the lower limit is 6.1 fish below the mean. Also note that you can’t just back-transform the confidence interval and add or subtract that from the back-transformed mean; you can’t take 100.344 and add or subtract that.
Square-root transformation. This consists of taking the square root of each observation. The back transformation is to square the number. If you have negative numbers, you can’t take the square root; you should add a constant to each number to make them all positive.
People often use the square-root transformation when the variable is a count of something, such as bacterial colonies per petri dish, blood cells going through a capillary per minute, mutations per generation, etc.
# Box-Cox transformation was previously run
data_for_models_transformed <-
data_for_models %>%
mutate(
# Plant's performance
total_biomass_sqrt = sqrt(total_biomass),
above_biomass_sqrt = sqrt(above_biomass),
below_biomass_log = log(below_biomass),
agr_log = log(agr),
# NO TRANSFORMATION variable already in log-log
rgr = rgr,
# NO TRANSFORMATION variable already in log-log
rgr_slope = rgr_slope,
# Traits
amax_log = log(amax),
gs_sqrt = sqrt(gs),
wue_log = log(wue),
# d13 and d15 where not transformed because the data has negative values
pnue_log = log(data_for_models$pnue),
# Covariate
init_height = log(init_height)) %>%
# Remove original variables (non-transformed)
dplyr::select(spcode, treatment, nfixer, init_height, everything(),
-c(5:8,11:13,16)) Models: Questions 1 and 2
\[response\sim treatment*fixer\ + initial\ height + random( 1|\ specie)\]
# Take response variables' names
response_vars_q1_q2 <-
set_names(names(data_for_models_transformed)[5:(ncol(data_for_models_transformed))])#data_for_models_transformed[data_for_models_transformed$id == 48,]
models_list_q1_q2 <- map(response_vars_q1_q2, ~ mixed_model_1(response = .x,
data = data_for_models_transformed))Models Nodule count
- Chapter 9 Mixed models in ecology check glmmML package for count data
- GOOD ref https://www.dataquest.io/blog/tutorial-poisson-regression-in-r/
- #https://www.flutterbys.com.au/stats/tut/tut11.2a.html
# Load data
# This step was done like this because I am working with a subset of the data
# source cleaned data
source("./scripts/code_clean_data_nodules.R")
# Delete unused variables
data_nodules_cleaned <-
data_nodules_cleaned %>%
# add id to rownames for keep track of the rows
column_to_rownames("id") %>%
dplyr::select(spcode,treatment, everything())# Boxcox for nodule count
BoxCoxTrans(data_nodules_cleaned$number_of_root_nodulation) Box-Cox Transformation
48 data points used to estimate Lambda
Input data summary:
Min. 1st Qu. Median Mean 3rd Qu. Max.
7.00 26.75 49.50 65.40 104.50 167.00
Largest/Smallest: 23.9
Sample Skewness: 0.689
Estimated Lambda: 0.1
With fudge factor, Lambda = 0 will be used for transformations
head(data_nodules_cleaned) spcode treatment number_of_root_nodulation
5 ec ambientrain 25
6 ec ambientrain 30
7 ec ambientrain 7
8 ec ambientrain 35
9 ec ambientrain_water_nutrients 11
10 ec ambientrain_water_nutrients 49
nodule_count_lab nodule_mass_in_the_lab average_nodule_weight
5 7 0.011 0.001571429
6 5 0.052 0.010400000
7 4 0.023 0.005750000
8 8 0.021 0.002625000
9 3 0.047 0.015666667
10 14 0.042 0.003000000
estimated_nodule_mass_per_plant init_height
5 0.039 17.0
6 0.312 25.0
7 0.040 14.0
8 0.092 16.0
9 0.172 20.5
10 0.147 21.0
m4 lmer gaussian
lmer_gaussian <- lmer(number_of_root_nodulation ~ treatment + init_height +
(1 |spcode),
data = data_nodules_cleaned)lmer_gaussian_log <- lmer(log(number_of_root_nodulation) ~ treatment + init_height +
(1 |spcode),
data = data_nodules_cleaned)m5 glmer poisson
glmer_poisson <- glmer(number_of_root_nodulation ~ treatment + init_height +
(1 |spcode), family = "poisson",
data = data_nodules_cleaned)models_list_nodule_count <- list(lmer_gaussian, lmer_gaussian_log, glmer_poisson)
names(models_list_nodule_count) <- c("lmer_gaussian",
"lmer_gaussian_log",
"glmer_poisson")Mycorrhizal colonization
I decided not to include it, because I want to focus on Nfixing vrs non-Fixing,
also I don't trust on the dataModels: Question 3
\[performance\sim treatment*\ fixer*\ scale(log(trait)\ + initial\ height + random( 1|\ specie)\]
Scale preditors
data_for_models_transformed_scaled <-
data_for_models_transformed %>%
# test for being sure that I select the traits
#select(c(4,7,8,13:16))
# scale only the predictors traits
mutate(across(c(4,7,8,13:16), scale))# Select traits (x_vars)
traits_names <-
set_names(names(data_for_models_transformed_scaled)
[c(7,8,13:16)])
traits_names d13c d15n amax_log gs_sqrt wue_log pnue_log
"d13c" "d15n" "amax_log" "gs_sqrt" "wue_log" "pnue_log"
# Select plants performance vars (y_vars)
performance_names <-
set_names(names(data_for_models_transformed_scaled)[c(5,6,9:12)])
performance_names rgr rgr_slope total_biomass_sqrt
"rgr" "rgr_slope" "total_biomass_sqrt"
above_biomass_sqrt below_biomass_log agr_log
"above_biomass_sqrt" "below_biomass_log" "agr_log"
models_lmer_formulas <- model_combinations_formulas(performance_names, traits_names)
length(models_lmer_formulas)[1] 36
models_list_q3 <- map(models_lmer_formulas,
~ lmer(.x, data = data_for_models_transformed_scaled))Validation plots
Collinearity
map(models_list_q1_q2, check_collinearity)$rgr
# Check for Multicollinearity
Low Correlation
Term VIF Increased SE Tolerance
treatment 3.97 1.99 0.25
nfixer 1.04 1.02 0.96
init_height 1.09 1.04 0.92
treatment:nfixer 3.92 1.98 0.26
$rgr_slope
# Check for Multicollinearity
Low Correlation
Term VIF Increased SE Tolerance
treatment 3.97 1.99 0.25
nfixer 1.05 1.02 0.95
init_height 1.09 1.04 0.92
treatment:nfixer 3.93 1.98 0.25
$d13c
# Check for Multicollinearity
Low Correlation
Term VIF Increased SE Tolerance
treatment 3.92 1.98 0.25
nfixer 1.21 1.10 0.83
init_height 1.08 1.04 0.93
treatment:nfixer 4.29 2.07 0.23
$d15n
# Check for Multicollinearity
Low Correlation
Term VIF Increased SE Tolerance
treatment 3.87 1.97 0.26
nfixer 1.73 1.32 0.58
init_height 1.07 1.03 0.94
Moderate Correlation
Term VIF Increased SE Tolerance
treatment:nfixer 5.53 2.35 0.18
$total_biomass_sqrt
# Check for Multicollinearity
Low Correlation
Term VIF Increased SE Tolerance
treatment 3.94 1.98 0.25
nfixer 1.16 1.07 0.87
init_height 1.08 1.04 0.92
treatment:nfixer 4.17 2.04 0.24
$above_biomass_sqrt
# Check for Multicollinearity
Low Correlation
Term VIF Increased SE Tolerance
treatment 3.96 1.99 0.25
nfixer 1.07 1.03 0.94
init_height 1.09 1.04 0.92
treatment:nfixer 3.97 1.99 0.25
$below_biomass_log
# Check for Multicollinearity
Low Correlation
Term VIF Increased SE Tolerance
treatment 3.92 1.98 0.26
nfixer 1.25 1.12 0.80
init_height 1.08 1.04 0.93
treatment:nfixer 4.38 2.09 0.23
$agr_log
# Check for Multicollinearity
Low Correlation
Term VIF Increased SE Tolerance
treatment 3.97 1.99 0.25
nfixer 1.05 1.03 0.95
init_height 1.09 1.04 0.92
treatment:nfixer 3.94 1.98 0.25
$amax_log
# Check for Multicollinearity
Low Correlation
Term VIF Increased SE Tolerance
treatment 3.96 1.99 0.25
nfixer 1.07 1.04 0.93
init_height 1.09 1.04 0.92
treatment:nfixer 3.98 2.00 0.25
$gs_sqrt
# Check for Multicollinearity
Low Correlation
Term VIF Increased SE Tolerance
treatment 3.85 1.96 0.26
nfixer 2.04 1.43 0.49
init_height 1.06 1.03 0.94
Moderate Correlation
Term VIF Increased SE Tolerance
treatment:nfixer 6.28 2.51 0.16
$wue_log
# Check for Multicollinearity
Low Correlation
Term VIF Increased SE Tolerance
treatment 3.90 1.97 0.26
nfixer 1.36 1.17 0.74
init_height 1.07 1.04 0.93
treatment:nfixer 4.64 2.15 0.22
$pnue_log
# Check for Multicollinearity
Low Correlation
Term VIF Increased SE Tolerance
treatment 3.90 1.98 0.26
nfixer 1.33 1.15 0.75
init_height 1.08 1.04 0.93
treatment:nfixer 4.58 2.14 0.22
map(models_list_nodule_count, check_collinearity)$lmer_gaussian
# Check for Multicollinearity
Low Correlation
Term VIF Increased SE Tolerance
treatment 1.06 1.03 0.94
init_height 1.06 1.03 0.94
$lmer_gaussian_log
# Check for Multicollinearity
Low Correlation
Term VIF Increased SE Tolerance
treatment 1.06 1.03 0.95
init_height 1.06 1.03 0.95
$glmer_poisson
# Check for Multicollinearity
Low Correlation
Term VIF Increased SE Tolerance
treatment 1.08 1.04 0.93
init_height 1.08 1.04 0.93
#Warning: Model has interaction terms. VIFs might be inflated. You may check
#multicollinearity among predictors of a model without interaction terms.
#map(models_list_q3, check_mul)Bolker’s plots
bolker_validation <- function(model) {
a <- plot(model, type = c("p", "smooth"))
## heteroscedasticity
b <- plot(model,sqrt(abs(resid(.))) ~ fitted(.), type = c("p", "smooth"))
cowplot::plot_grid(a,b,nrow = 1)
}Models for questions 1,2
map(models_list_q1_q2, bolker_validation)$rgr
$rgr_slope
$d13c
$d15n
$total_biomass_sqrt
$above_biomass_sqrt
$below_biomass_log
$agr_log
$amax_log
$gs_sqrt
$wue_log
$pnue_log
Models for nodule count
map(models_list_nodule_count, bolker_validation)$lmer_gaussian
$lmer_gaussian_log
$glmer_poisson
Models for question 3
map(models_list_q3, bolker_validation)$`abovebiomasssqrt~amaxlog`
$`abovebiomasssqrt~d13c`
$`abovebiomasssqrt~d15n`
$`abovebiomasssqrt~gssqrt`
$`abovebiomasssqrt~pnuelog`
$`abovebiomasssqrt~wuelog`
$`agrlog~amaxlog`
$`agrlog~d13c`
$`agrlog~d15n`
$`agrlog~gssqrt`
$`agrlog~pnuelog`
$`agrlog~wuelog`
$`belowbiomasslog~amaxlog`
$`belowbiomasslog~d13c`
$`belowbiomasslog~d15n`
$`belowbiomasslog~gssqrt`
$`belowbiomasslog~pnuelog`
$`belowbiomasslog~wuelog`
$`rgr~amaxlog`
$`rgr~d13c`
$`rgr~d15n`
$`rgr~gssqrt`
$`rgr~pnuelog`
$`rgr~wuelog`
$`rgrslope~amaxlog`
$`rgrslope~d13c`
$`rgrslope~d15n`
$`rgrslope~gssqrt`
$`rgrslope~pnuelog`
$`rgrslope~wuelog`
$`totalbiomasssqrt~amaxlog`
$`totalbiomasssqrt~d13c`
$`totalbiomasssqrt~d15n`
$`totalbiomasssqrt~gssqrt`
$`totalbiomasssqrt~pnuelog`
$`totalbiomasssqrt~wuelog`
Performance package
Models for questions 1,2
map(models_list_q1_q2, check_model)$rgr
$rgr_slope
$d13c
$d15n
$total_biomass_sqrt
$above_biomass_sqrt
$below_biomass_log
$agr_log
$amax_log
$gs_sqrt
$wue_log
$pnue_log
Models for nodule count
map(models_list_nodule_count, check_model)$lmer_gaussian
$lmer_gaussian_log
$glmer_poisson
Models for question 3
map(models_list_q3, check_model)$`abovebiomasssqrt~amaxlog`
$`abovebiomasssqrt~d13c`
$`abovebiomasssqrt~d15n`
$`abovebiomasssqrt~gssqrt`
$`abovebiomasssqrt~pnuelog`
$`abovebiomasssqrt~wuelog`
$`agrlog~amaxlog`
$`agrlog~d13c`
$`agrlog~d15n`
$`agrlog~gssqrt`
$`agrlog~pnuelog`
$`agrlog~wuelog`
$`belowbiomasslog~amaxlog`
$`belowbiomasslog~d13c`
$`belowbiomasslog~d15n`
$`belowbiomasslog~gssqrt`
$`belowbiomasslog~pnuelog`
$`belowbiomasslog~wuelog`
$`rgr~amaxlog`
$`rgr~d13c`
$`rgr~d15n`
$`rgr~gssqrt`
$`rgr~pnuelog`
$`rgr~wuelog`
$`rgrslope~amaxlog`
$`rgrslope~d13c`
$`rgrslope~d15n`
$`rgrslope~gssqrt`
$`rgrslope~pnuelog`
$`rgrslope~wuelog`
$`totalbiomasssqrt~amaxlog`
$`totalbiomasssqrt~d13c`
$`totalbiomasssqrt~d15n`
$`totalbiomasssqrt~gssqrt`
$`totalbiomasssqrt~pnuelog`
$`totalbiomasssqrt~wuelog`
Save lists with the models
saveRDS(models_list_q1_q2, file = "./processed_data/models_q1_q2.RData")
saveRDS(models_list_q3, file = "./processed_data/models_q3_3_way_interaction.RData")
saveRDS(models_list_nodule_count, file = "./processed_data/models_list_nodule_count.RData")